PdxTaSe2 series is an excellent system for the investigation of the interplay between CDW and superconductivity which shows quantum critical point for x = 0.1. Very recently, we have studied 6% and 12% Pd doping samples of PdxTaSe2. We detect spontaneous fields in the ZF-µSR data only for the 6% Pd doping sample, most probably associated with time-reversal-symmetry (TRS) breaking superconducting state. This probably suggests that the exotic superconducting state observed in the 6% Pd doping sample is due to its interplay with CDW phase. However, a firm conclusion can only be reached if we are able to do a systematic study of the full phase diagram of the PdxTaSe2 series. Here we propose to study 3%, 8%, 10% and 15% Pd doping samples of the PdxTaSe2 series using the MuSR instrument. We ask for 8 days of MuSR beamtime to complete this project.